I think you may be vastly overestimating the scientific literacy of the general public.

I don't mean to imply that most people are stupid or anything. Far from it I've met many tradesman (and tradeswomen) who I consider vastly more intelligent than many people I've met with PhDs.

But, I suspect the willingness of most folks to care about the distinction you're making is negligible at best.

It's sort of like being a car salesman who truly loves cars. And the type of car you're selling has a brand new oil-pump bearing design that is 30% more efficient than the prior bearing design. It doesn't make much of a difference in the overall performance of the car, but you're fascinated by the engineering prowess of it. Unfortunately, 99.9% of the people who walk in the dealership simply don't care about the oil pump bearing. They care about the heated seats, and the bluetooth audio, and if they can get it in seafoam green with the black trim package.

In a similar fashion, although I find knockout mice to be absolutely fascinating (to steal your example), my friends and family simply glaze over when I start to ramble on about such things. They simply don't care. But when they need the gene therapy that resulted from studies performed with the knockout mice for their weird cancer, well, then they're interested (but not too much).

And, so, most people don't know a for loop, from a plasmid, from a cloud chamber, from a difference-in-differences regression equation in economics research. And as a result, they're not even remotely interested in the degree of stochastic factors that may be influencing the research design of the study poorly-summarized in the Medium article that pops up on their Facebook feed.

I would love for people to be more savvy in interpreting the products of the scientific method (or any variation thereof) that they may encounter. But most people are so far behind in being able to approach such detours into the methodology that such a semantic distinction would prove useless. Hell, I have more years in grad school under my belt than I care to admit, and even I will tell anyone who will listen that I barely understand most stuff outside of my field. A political science paper utilizing network models to analyze trade fluctuations with third-party nations following bilateral trade agreements. Maybe I could get the gist of it, but I'm probably not confident enough to definitively say if it's bullshit or not.

Rather, I argue that we focus on piquing the public's curiosity, and doing our damndest to act as scientific ambassadors to the next generation. Rather than changing what we classify as 'science' in the colloquial sense, give a nephew or niece a copy of Calculus Made Easy (and actually help them get through it), show them how to use a metal lathe, give them a brief demonstration of OLS regression by hand, get them a decent microscope to look at pond water with, build a TTL flip-flop with them on a breadboard, and read them The Logic of Collective Action as a bedtime story for the hell of it. The only way we lift the ability of the general public to understand the application of the scientific method in all of it's forms, is by teaching the general public to give a shit about it in the first place. For most people, it's just too late, but it's certainly not too late for us as a collective society.